Textbook Problem

Median Age The table shows the median ages of the U.S. resident population for the years 2005 through 2013. (Source: U.S. Census Bureau)

Year	2005	2006	2007	2008	2009
Median age	36.2	36.3	36.5	36.7	36.8
Year	2010	2011	2012	2013
Median age	37.2	37.3	37.5	37.6

Spreadsheet at LarsonAppliedCaIculus.com

(a) Use Simpson’s Rule to estimate the average median age over the time period.

(b) A model for the data is

$A=37.2-0.54t+0.084t^2-0.0031t^3$ for $5\le t\le 13$, where A is the median age and t is the year, with $t=5$ corresponding to 2005. Use integration to find the average median age over the time period.

(c) Compare the results of parts (a) and (b).